In addition to being a framework for design and behaviour generation / selection in autonomous systems, the concept of the well-being of a system can be quantified by computing aggregate measures of theneedsandemotionsof a system. These would serve as metrics for comparing systems, even those not implemented using theSurvivability Framework. Several forms of metrics for measurement of the well-being of a system are described as follows. These are the balanced needs aggregate, root-mean-square aggregate priority-weighted needs aggregate, weakest-link needs aggregate, and the inverted-priority needs aggregate.
B.1.1 Balanced Needs Aggregate (BNA)
The balanced needs aggregate (BNA) is based on the average of the current levels of needs fulfilment, for all different needs of a system, given by:
ABN A(k) = 1 M
M
X
i=1
¯
ni(k); M =|n|. (B.1)
This gives an overall measure of thewell-being of a system, but it does not account for relative degrees of importance between needs. However, in situations when the relative importance between needs are unknown, this measure remains useable.
B.1.2 Root Mean Square Needs Aggregate (RMSA)
The root-mean-square needs aggregate (MSNA) is based on the root-mean-square of current levels of needs fulfilment, for all different needs of a system, given by:
ARM SA(k) = r 1
M XM
i=1[¯ni(k)]2. (B.2) This metric de-emphasizes lower values of fulfilment in favour of higher fulfilment levels, which has the effect of shifting the aggregate value closer to the higher fulfilment levels.
B.1.3 Priority-weighted Needs Aggregate (PWNA)
In the priority-weighted needs aggregated (PWNA), it is assumed that the relative importance between needs are known. WithFP(ni(k))being an earlier defined function FP : N → [0,1]∩Rthat evaluates the relative importance of needs such that FP → 1 with increasing importance, PWNA can be computed as follows:
AP W N A(k) = PM
i=1FP(ni(k))¯ni(k) (M)PM
i=1FP(¯ni(k)) (B.3)
As compared to the BNA, PWNA is a closer reflection of the well-beingof a system in terms of giving higher weighage to needs of higher priority.
B.1.4 Weakest-link Needs Aggregate (WLNA)
The weakest-link needs aggregate (WLNA) is computed from the minimum level of needs fulfilment among all the needs of a system. It is based on the notion that a system’s survivability andwell-beingis only as good as the least-fulfilled need.
AW LN A(k) =min{n¯1(k), n¯2(k), ..., n¯M(k)} (B.4) B.1.5 Inverted-priority Needs Aggregate (IPNA)
The inverted-priority needs aggregate (IPNA) is similar to WLNA, with the inclusion of the inverse priority functionF¯P(ni(k)) = 1−FP(ni(k)). It is given as:
AIP N A(k) = TM
i=1[ ¯FP(ni(k))]¯ni(k)
1 M
PM
i=1[ ¯FP(ni(k))] (B.5) IPNA is intended to discount the contribution of a need’s fulfilment to the aggregate if it does not have a relatively higher priority. It differs from WLNA in that the need that is least fulfilled may not necessarily have a significant impact on the aggregate, if it is not of a high priority. For instance, a fulfilment of0.1is more significant to a need with higher priority (e.g.0.5) than one with lower priority (e.g. 0.2).
B.1.6 Analytical example
Consider the following example to understand the differences between the metrics (Table B.1). In this example, case (a) and (b) have the same aggregate for BNA, despite differences in the fulfilment between needs. The BNA, RMSA and WLNA metrics are invariant with the relative priorities of needs. In both cases, the same aggregate value for WLNA is coincidental, since0.2is the lowest level of needs fulfilment in either case.
The RMSA as compared to the BNA, gives higher weighage to larger values of needs fulfilment, regardless of priority. This is one of the properties of the root-mean-square
Table B.1: Analytical example of survivability metrics.
Metric sustenance safety awareness accomplishment cognition
(a) Fulfilment 0.5 0.4 0.3 0.4 0.2
Priority 0.5 0.4 0.3 0.2 0.1
BNA ABN A=0.5 + 0.4 + 0.3 + 0.4 + 0.2
5 = 0.36
RMSA ARM SA=
r
0.52+ 0.42+ 0.32+ 0.42+ 0.22
5 = 0.374
PWNA AP W N A= 0.5(0.5) + 0.4(0.4) + 0.3(0.3) + 0.2(0.4) + 0.1(0.2)
(0.5 + 0.4 + 0.3 + 0.2 + 0.1) = 0.4
WLNA AW LN A=min{0.5, 0.4, 0.3, 0.4, 0.2} = 0.2
IPNA AIP N A=
T
{0.5(0.5), 0.6(0.4), 0.7(0.3), 0.8(0.4), 0.9(0.2)}
(0.5 + 0.6 + 0.7 + 0.8 + 0.9)/5 = 0.257
(b) Fulfilment 0.2 0.5 0.3 0.2 0.6
Priority 0.5 0.4 0.3 0.2 0.1
BNA ABN A=0.2 + 0.5 + 0.3 + 0.2 + 0.6
5 = 0.36
RMSA ARM SA=
r
0.22+ 0.52+ 0.32+ 0.22+ 0.62
5 = 0.395
PWNA AP W N A= 0.5(0.2) + 0.4(0.5) + 0.3(0.3) + 0.2(0.2) + 0.1(0.6)
(0.5 + 0.4 + 0.3 + 0.2 + 0.1) = 0.327
WLNA AW LN A=min{0.2, 0.5, 0.3, 0.2, 0.6} = 0.2
IPNA AIP N A=
T
{0.5(0.2), 0.6(0.5), 0.7(0.3), 0.8(0.2), 0.9(0.6)}
(0.5 + 0.6 + 0.7 + 0.8 + 0.9)/5 = 0.143
function, and observed in both cases, where due to the presence of needs with higher fulfilments, the values ofARM SA> ABN A.
Priority-weighted metrics such as PWNA gives greater emphasis on the fulfilment values of needs of higher priority. In case (a), this results in a value ofAP W N A(= 0.4)>
ABN A(= 0.36), which is due to needs with higher priorities having higher values of fulfilment. The opposite is true of case (b), where AP W N A(= 0.327) < ABN A(= 0.36) due to lower fulfilment of needs with higher priorities. Of special note is the IPNA, which uses the inverse priority function. While similar to WLNA in nature (i.e. it is a minimum-value filter), the operation of the inverse priority function prevents needs with low fulfilment and priorities from being selected, i.e. it determines the minimum aggregate values among only needs which “matter more” (namely, those of higher priorities).
A PPENDIX C
Systems and Demonstrators